Description

琪琪在大海上搜索涛涛，琪琪把大海分为2500*2500的网格，现在琪琪拥有N条小帆船，她可以在船之间移动，由于风向的原因，她只能从一条船移动到位于这条船严格左上方或严格右下方的船。对于

每条帆船，琪琪想要知道从这条船跳到其他各条船的最小跳转次数和。

Format

Input

The first line of input contains an integer * N* (3 ≤ N ≤ 250 000), the number of islands. The following * N* lines

contain the locations of the islands. Each location is a pair of integers between 1 and 2500 (inclusive), the row and column numbers, respectively.

第一行包含一个数N，表示帆船的个数。 接下来的N行，每行包含一对数(x,y)，表示帆船的位置

Output

The output should contain * N* lines. For each island, in the same order they were given in the input, output

the sum of sailing distances from all other islands on a single line.

输出需要包含N行，表示琪琪想要知道的答案。

Samples

7
1 7
7 5
4 5
4 8
6 6
6 1
2 3

16
11
12
11
12
16
8